How the Checkerboard Shadow Illusion works:

If this illusion were a real-world object, then yes, the A-Tile would obviously be much darker than the B-Tile. Your brain naturally understands that things don't actually change color just because of light or shadow. A bright tile doesn't physically change just because it is in a shadow, just as a dark tile doesn't change if it's in the light.

However, this interpretation is misleading when you try and compare the actual values of light and dark that your eyes see. The illusion is constructed so that the intensity of the light tile in 'shadow' perfectly matches the intensity of the dark tile in the 'light'. Your brain is fooled as it tries to compensate for the artificial shadow over the checkered pattern.